Proving Two Partition Identities

Robson da Silva, Jair Cunha Filho, José Plínio Oliveira Santos

Abstract


In this paper we give combinatorial proofs for two partition identities. The first one solves a recent open question formulated by G. E. Andrews.

References


G.E. Andrews, “The Theory of Partitions”, Cambridge University Press, 1984.

G.E. Andrews, Parity in partition identities, The Ramanujan Journal, 23 (2010), 45–90.

J.C. Filho, “Variações do Diagrama de Ferrers, Partições Planas e Funções Geradoras”, Tese de Doutorado, IMECC, UNICAMP, Campinas, SP, 2006.

H. Göllnitz, "Einfache Partionen", Diplomarbeit W.S. 1960, Göttingen, 65 pp.

H. Göllnitz, Partitionen mit Differenzenbedingungen, J. Reine Angew. Math, 225(1967), 154-190.

B. Gordon, Some Ramanujan-like continued fractions, Abstracts of Short Communications, Int. Congr. of Math., 29-30, Stockholm, 1962.

B. Gordon, Some continued fractions of the Rogers-Ramanujan type, Duke Math. J., 31 (1965), 741-748.

A.J. Yee, Ramanujan’s partial theta series and parity in partitions, The Ramanujan Journal, 23 (2010), 215–225.




DOI: https://doi.org/10.5540/tema.2012.013.02.0133

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Trends in Computational and Applied Mathematics

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